Add this function to your WordPress theme's `functions.php` file and call it from `archive.php` using the template tag `my_archive_post_count()`. If $echo parameter is set to false, it will simply return the HTML as a string. Post count is appended with previous- and next page links if there is more than one page.

wordpress-archive-post-count.php

<?php

function my_archive_post_count( $echo = true ) {
    global $wp_query;
    $showing = '';
    
    if ( $wp_query->found_posts > 1 ) {
        // Get previous & next page links.
        $args = array(
            'sep'      => ' &#8212; ',
            'prelabel' => __('&laquo; Previous'),
            'nxtlabel' => __('Next &raquo;'),
        );
        $page_links  = get_posts_nav_link( $args );
        
        // Calculate post range based on posts per page and total posts found.
        $page_number = is_paged() ? $wp_query->query_vars['paged'] : 1;
        $current_max = ( get_option( 'posts_per_page' ) * ( $page_number - 1 ) ) + $wp_query->post_count;
        $current_min = $current_max - $wp_query->post_count + 1;
        
        // Prepare post counts for display.
        $range   = ( $current_min == $current_max ) ? strval( $current_min ) : $current_min . '-' . $current_max;
        $total   = $wp_query->found_posts;
        
        // Create HTML string for output.
        $showing =
            '<div class="showing" style="margin-right:1em;">'
            . 'Currently viewing ' . $range . ' of ' . $total . ' articles. '
            . $page_links . '<div>'
        ;
    }
    if ( true === $echo ) echo $showing;
    return $showing;
}

The original version did not accurately calculate post counts on the last page; updating it now and turning it into a function.

Thanks man, this came in useful for me, though I didn't use it on the archives page, I used it to display the count of posts on the index.php.

Saved my day! :)